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We propose and analyze a new parallel coordinate descent method---`NSync---inwhich at each iteration a random subset of coordinates is updated, in parallel,allowing for the subsets to be chosen non-uniformly. We derive convergencerates under a strong convexity assumption, and comment on how to assignprobabilities to the sets to optimize the bound. The complexity and practicalperformance of the method can outperform its uniform variant by an order ofmagnitude. Surprisingly, the strategy of updating a single randomly selectedcoordinate per iteration---with optimal probabilities---may require lessiterations, both in theory and practice, than the strategy of updating allcoordinates at every iteration.

On Optimal Probabilities in Stochastic Coordinate Descent Methods